(1) Field of the Invention
The present invention relates to a system and method for detecting signals in noise. More specifically, the present invention relates to the detection of unknown broadband signals in noise consisting of non-stationary narrowband components and a stationary colored broadband component.
(2) Description of the Prior Art
Many applications require the identification of a desired signal within undesired random signals (noise) which is received with and often interferes with the desired signal. For example, in sonar systems randomly generated sounds from both natural and man made sources give rise to a noise that interferes with desired acoustic signals. To detect and identify a specific contact, such as an underwater vehicle, requires a system which can detect a signal corresponding to a contact within received data containing both the signal and undesired signals (noise). Similarly, in communications systems control signals must be differentiated from the data signals which are carried on the same channels.
Received data is modeled as the sum of a signal component and a noise component. When information about the signal and/or noise components is known or can be accurately presumed, several methods are often available to choose from in constructing a robust signal detector. For example, if the probability density function and spectrum of the signal and noise components are known, it is possible to construct an optimum detector using either Neyman-Pearson or uniformly most powerful invariant detection methods. With sufficient signal information known, detecting and extracting desired signals in noise is a relatively straight-forward exercise.
However, in many applications nothing is known about either the signal or the noise components present. In applications where nothing is known about the signal or noise components, a commonly used receiver is an energy detector given by:                               ∑                      k            =            1                    N                ⁢                                            "LeftBracketingBar"                              X                k                            "RightBracketingBar"                        2                    ⁢                                                                                                                                                                                                                            signal                              ⁢                                                              xe2x80x83                                                            ⁢                              present                                                                                                                                                             greater than                                                                                                                                                                           ≤                                                                                                                                            signal                  ⁢                                      xe2x80x83                                    ⁢                  absent                                                              ⁢          λ                                    (        1        )            
where Xk is the kth data DFT bin                                           X            k                    =                                                    ∫                τ                            ⁢                        ⁢                          x              ⁡                              (                t                )                                      ⁢                          ⅇ                                                -                  ⅈ2π                                ⁢                                                      (                                          k                      -                      1                                        )                                    τ                                                      ⁢                          xe2x80x83                        ⁢                          ⅆ              t                                      ,                            (        2        )            
x(t)=s(t)+n(t) is the received data and xcex is a threshold. The energy detector performs well and is quite suited for many applications. Additionally, the energy detector is non-parametric, requiring almost no prior knowledge about the signal. However, the energy detector, which is optimum when the signal occupies the entire Nyquist bandwidth, performs poorly when the signal has small bandwidth relative to the Nyquist rate. The energy detector also performs poorly when the noise component contains colored noise.
Recently, use of power law detectors for detection of unknown signals has been proposed. A power law detector for detecting a Gaussian signal in Gaussian noise is given by:                               ∑                      k            =            1                    N                ⁢                                            (                                                "LeftBracketingBar"                                      X                    k                                    "RightBracketingBar"                                2                            )                        v                    ⁢                                                                                                                                                                                                                            signal                              ⁢                                                              xe2x80x83                                                            ⁢                              present                                                                                                                                                             greater than                                                                                                                                                                           ≤                                                                                                                                            signal                  ⁢                                      xe2x80x83                                    ⁢                  absent                                                              ⁢          λ                                    (        3        )            
where the power xcexd is a positive real number. If a signal is present, the signal will occupy an arbitrary set of M out of a total of N DFT bins. With the power xcexd appropriately chosen, the power law detector significantly outperforms energy detectors (equation (1)) when the normalized-signal bandwidth is small (i.e., M/N less than  less than 1). However, when signal bandwidth is large, the power law detector is slightly out performed by the energy detector. As can be seen when the power xcexd is one, the power law detector is identical to the energy detector.
Although the power law detector provides improved performance, as compared to that of the energy detector, it suffers from several disadvantages which limits its use for many applications. For example, the power law adapter assumes the noise component n(t) is white which is not true for most applications. Additionally, the power law detector is inherently sensitive to interfering tonals. Furthermore, prewhitening, using conventional periodogram-based or inversecovariance techniques is not practical for several reasons.
For instance, in many applications, the tonal components tend to be highly non-stationary due to channel variability and source and receiver motion which makes tonal amplitude or power difficult to estimate. Over resolution of the spectral microstructure, which is inherently unstable due to non-stationarity, and frequency drifting due to source and receiver motion results in inaccurate estimates of the spectrum. Additionally, periodogram-based methods using smoothers work poorly in the presence of closely spaced tones and high sidelobe leakage. Unpredictable smearing, biases, and leakage effects due to windowing are also inherent in periodogram-based methods.
Thus, what is needed is a signal detector capable of detecting unknown signals over a range of bandwidths within received data having both white and colored noise components.
Accordingly, it is a general purpose and object of the present invention to provide system and method for detecting unknown signals in noise which does not require knowledge of either the signal to be detected or the noise present.
Another object of the present invention is to provide a system capable of detecting unknown signals over a wide range of bandwidths when the received data contains both white and colored noise.
A further object of the present invention is the provision of system and method for detecting unknown broadband signals in noise consisting of non-stationary narrowband components and a stationary colored broadband component.
These and other objects made apparent hereinafter are accomplished with the present invention by a system which uses a non-parametric adaptive power law detector operating on a normalized (whitened) broadband signals to detect unknown broadband signals in noise. A sensor collects data in which a signal of interest may be found and generates a received data stream. A preprocessor operates on the received data stream to generate data vectors xT and xD corresponding to training (noise only) and detection (noise plus signal) intervals of the received data stream, respectively. A spectrum processor receives the training and detection vectors and generates cleaned broadband spectrum estimates {tilde over (C)}1(ƒ) and {tilde over (C)}2(ƒ) of the xT and xD vectors, respectively, by adaptively separating non-stationary tonal components from the stationary broadband component using modified multiple taper spectral estimation combined with maximum likelihood tonal removal. The cleaned broadband spectrum estimates {tilde over (C)}1(ƒ) and {tilde over (C)}2(ƒ) are passed to a detection processor which uses the spectrum estimates as input to a non-parametric power law detection process given by the test statistic:                               ∑          n                ⁢                                            (                                                                                          C                      ~                                        2                                    ⁡                                      (                                          f                      n                                        )                                                                                                              C                      ~                                        1                                    ⁡                                      (                                          f                      n                                        )                                                              )                        v                    ⁢                                                                                                                                                                                                                            signal                              ⁢                                                              xe2x80x83                                                            ⁢                              present                                                                                                                                                             greater than                                                                                                                                                                           ≤                                                                                                                                            signal                  ⁢                                      xe2x80x83                                    ⁢                  absent                                                              ⁢          λ                                    (        4        )            
When a signal is present, the detection processor produces an output signal which indicates the number and location of the n DFT bins occupied by the signal.